An analytical Prj2CR covariance estimation method for iterative CT reconstruction algorithms

Abstract

Image mean and covariance required for a model observer are usually calculated by the statistical method using image samples, which is hard to acquire in reality. Although some analytical methods are proposed to estimate image covariance from a single projection, these methods are of high computational cost for large-dimensional images (e.g., 512×512), and images of large dimension are commonly required. Considering the covariance used for a model observer is the covariance of the channel response, whose dimension is much smaller than the image covariance, we aim to obtain the covariance of small-dimensional channel response directly from its projection. Channel filters are applied to the analytical projection to image (Prj2Img) covariance estimation method to derive the analytical projection to channel response (Prj2CR) covariance estimation method, which successfully reduces the computational cost and connects the covariance of projection and channel response. In addition, a transition matrix is introduced in Prj2CR method to stabilize the connections. The transition matrix mainly depends on channel filters, not the system, phantom, and reconstruction algorithm, which means it can be calibrated by small-dimensional reconstructions and then applied to any situation with a same channel filter. We validate the feasibility and utility of the proposed Prj2CR method by simulations. 128×128 reconstructions from qGGMRF-WLS are adopted for calibration, while 512×512 reconstructions are used for validation. SNR of CHO is chosen as the figure of merit for performance evaluation, and the covariance estimated by 290 image samples are used as the reference. Results show that the SNR by the Prj2CR method is within 95% confidence interval of the SNR* by 290 image samples, indicating that the proposed method accords with statistical method. The Prj2CR method may be beneficial for subjective image quality assessment since it only needs a single sample of projection and has low computational cost.